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Title: Deformed Cartan matrices and generalized preprojective algebras II: general type
Authors: Fujita, Ryo  kyouindb  KAKEN_id  orcid https://orcid.org/0000-0003-4905-2402 (unconfirmed)
Murakami, Kota
Author's alias: 藤田, 遼
村上, 浩大
Keywords: Deformed Cartan matrices
Braid group actions
Generalized preprojective algebras
Categorifications
16G20
17B37
16W50
17B67
81R50
Issue Date: Dec-2023
Publisher: Springer Nature
Journal title: Mathematische Zeitschrift
Volume: 305
Issue: 4
Thesis number: 63
Abstract: We propose a definition of deformed symmetrizable generalized Cartan matrices with several deformation parameters, which admit a categorical interpretation by graded modules over the generalized preprojective algebras in the sense of Geiß–Leclerc–Schröer. Using the categorical interpretation, we deduce a combinatorial formula for the inverses of our deformed Cartan matrices in terms of braid group actions. Under a certain condition, which is satisfied in all the symmetric cases or in all the finite and affine cases, our definition coincides with that of the mass-deformed Cartan matrices introduced by Kimura–Pestun in their study of quiver W-algebras.
Rights: © The Author(s) 2023
This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
URI: http://hdl.handle.net/2433/286956
DOI(Published Version): 10.1007/s00209-023-03386-4
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